The invention relates to the field of portable electric lamps, including lamps called “headlamps” which are worn on the forehead so as to perform lighting in the forward direction, being for example able to be fitted on a helmet. More precisely, the invention relates to an electric power supply device for supplying electric power to a portable lamp, of the kind comprising an enclosure and electric connections for connection, in a power supply circuit, with either one of two interchangeable electric power sources, as required, that are a rechargeable storage battery and a set of at least two primary cells. In the electric power supply device of the kind considered here, the electric connections comprise a contact for connecting a terminal of one of the primary cells to a terminal of the other primary cell, whereas the enclosure delineates a housing for accommodating either the primary cells together or the rechargeable storage battery.